View Single Post
Old 2021-05-15, 04:04   #2
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

2×3×54 Posts
Default

  • kronecker(a^2-4*a,n)==-1
  • kronecker(a^2+4*a,n)==-1
  • a^((n-1)/2)==kronecker(a,n) (mod n)
  • x^((n+1)/2)==kronecker(a,n) (mod n, x^2-(a-2)*x+1)
  • x^((n+1)/2)==kronecker(-a,n) (mod n, x^2+(a+2)*x+1)
  • gcd(a^2-1,n)==1
Those n below 4*10^6 requiring gcd(a^2-1,n) are so few I can list them here:

Code:
[5777, 1854, 5777]                                                            
[17261, 420, 421]                                                             
[17261, 843, 421]
[17261, 3790, 421]
[17261, 5053, 421]
[113573, 48910, 113573]
[120581, 2942, 2941]
[120581, 5881, 2941]
[120581, 21453, 2941]
[120581, 26468, 2941]
[120581, 30276, 2941]
[120581, 35291, 2941]
[120581, 50863, 2941]
[120581, 59686, 2941]
[1033997, 317611, 1033997]
[1729331, 422433, 13201]
[1842581, 269647, 44941]
[1842581, 449411, 44941]
[1842581, 539291, 44941]
[1842581, 584232, 44941]
[3774377, 1256294, 3774377]
[3900797, 1544479, 3900797]

Last fiddled with by paulunderwood on 2021-05-15 at 04:15
paulunderwood is online now   Reply With Quote